ECN 741: Public EconomicsFall 2008Differentiate w.r.tαand setα= 1we get∑nk=1UikckUi=∑nk=1UjkckUjAlso, note thatUl=Wl,Uli=WlgGiandUi=WgGi. Therefore,Hi=-∑nk=1UikckUi-UillUi=-∑nk=1UikckUi-WlglWg=HjThis can be generalized to utility functions of the formu(c1, . . . , ck, G(ck+1, . . . , cn), l)in which,G(·)is homothetic. Then the result is that commodities(ck+1, . . . , cn)should betaxed at uniform rate.Exercise:Suppose consumer is endowed withyunit of good one that cannot be taxedaway.Does the uniform commodity taxation still hold?what if the utility function isadditive separable?Exercise:Suppose government is restricted to setting taxed onc1to zero.How wouldmodify the Ramsey problem? Does the uniform commodity taxation hold?
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Trigraph, Uniform commodity taxation, Uik ck, Uik ck Wlg